Can it be valid to standardize non-normal data going into a PCA?

Question

I have a collection of highly non-normal behavioral variables measured for each animal in a given test. I would like to reduce to 2 or 3 scores to characterize the individual's test using PCA. I see in the literature where others have referenced Multivariate Statistics books to justify using non-normal data for this kind of use of PCA. The measures are in very different scales of units (e.g. one that runs to 30, others in the tens of thousands). If I use [R] prcomp with centering and scaling on my non-normal raw data, the resulting PC loadings make biological sense. But can one center and scale non-normal data like this?